On the feasibility of spherical magnetic liquid mirror telescopes

Abstract

Liquid mirror telescopes exploit the rotation of a reflective fluid to generate diffraction-limited parabolic surfaces. They are economical and scalable but limited to zenith pointing. To expand their field of view, liquid mirror surfaces may be actuated into a spherical cap by means of magnetically susceptible liquids and electromagnetic coils, allowing the optics to rotate without actuating the mirror. However, the practical implementation of the concept remains largely unexplored. This paper adopts a nonlinear ferrohydrodynamic model to explore the technical feasibility of spherical liquid mirror telescopes. Surface deviations for a limited number of coils are extrapolated to determine the magnetic configuration requirements for a given optical wavelength, leading to an expected necessary coil count of $16\pm 12$ for a mirror capable of operation in the visible spectrum, and $13\pm 10$ for one operating in the mid-infrared. Tolerances of $7.3\mu m$ for coil positioning, 6.0 A for coil currents, and 9.1 nrad s⁻¹ for mirror spinning speed are required with coil currents of up to 20 MA to achieve the optical performance metrics using low-density ferrofluids. The results indicate that, although mathematically achievable, the required precision exceeds current technological capabilities, motivating alternative approaches to the problem.